尺寸减小(Dimension Reduction)

 我正在尝试将高维数据集缩减为2-D。 但是，我无法预先访问整个数据集。 因此，我想生成一个采用N维向量并返回二维向量的函数，这样如果我将它赋予在N维空间中接近的向量，则结果接近于二维向量空间。 
 
 我认为SVD是我需要的答案，但我不能让它发挥作用。 
 
 为简单起见，设N = 3，假设我有15个数据点。 如果我在15x3矩阵X中预先获得所有数据，那么： 
 
[U, S, V] = svd(X);
s = S; %s is a the reduced version of S, since matlab is case-sensitive.
s(3:end,3:end)=0;
Y=U*s;
Y=Y(1:2,:);
 
 做我想要的。 但是假设我得到一个新的数据点，A，1x3向量。 有没有办法使用U，S或V将A转换为适当的1x2向量？ 
 
 如果SVD是一个失败的原因，有人可以告诉我我应该做什么吗？ 
 
 注意：这是Matlab代码，但我不在乎答案是C，Java还是数学。 如果您无法阅读Matlab，请询问并澄清。 

I'm trying to reduce a high-dimension dataset to 2-D. However, I don't have access to the whole dataset upfront. So, I'd like to generate a function that takes an N-dimensional vector and returns a 2-dimensional vector, such that if I give it to vectors that are close in N-dimensional space, the results are close in 2-dimensional space.
 
I thought SVD was the answer I needed, but I can't make it work. 
 
For simplicity, let N=3 and suppose I have 15 datapoints. If I have all the data upfront in a 15x3 matrix X, then:
 
[U, S, V] = svd(X);
s = S; %s is a the reduced version of S, since matlab is case-sensitive.
s(3:end,3:end)=0;
Y=U*s;
Y=Y(1:2,:);
 
does what I want. But suppose I get a new datapoint, A, a 1x3 vector. Is there a way to use U, S, or V to turn A into the appropriate 1x2 vector?
 
If SVD is a lost cause, can someone tell me what I should be doing instead?
 
Note: This is Matlab code, but I don't care if the answer is C, Java, or just math. If you can't read Matlab, ask and I'll clarify.

原文：https://stackoverflow.com/questions/1538656